Individual-scale analysis

Pair-wise correlations

Between continuous variables: Pearson
Between a binary and a continuous variable: Mann-Whitney
Between binary variables: Chi-square

Latitude

Age

Altitud

BMI

Diabetes

Hypertension

Sugar

Vitamin D

Multiple regression 1

Response variable = vit D
Explanatory variables = bmi, lat, alt Only using data of women 20-49 (no BMI data for > 60)

## 
## Call:
## lm(formula = vitD ~ BMI + Lat + Altitude, data = df_vitd)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -49.186 -11.162  -1.078   9.929  78.566 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.031e+02  2.667e+00  38.665   <2e-16 ***
## BMI         -5.038e-01  5.760e-02  -8.746   <2e-16 ***
## Lat         -9.889e-01  8.768e-02 -11.279   <2e-16 ***
## Altitude    -6.342e-03  3.933e-04 -16.124   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.56 on 2393 degrees of freedom
##   (741 observations deleted due to missingness)
## Multiple R-squared:  0.1371, Adjusted R-squared:  0.136 
## F-statistic: 126.7 on 3 and 2393 DF,  p-value: < 2.2e-16

Multiple regression 2

Response variable = vit D
Explanatory variables = lat, alt Using all data (ages 20 - > 60)

## 
## Call:
## lm(formula = vitD ~ Lat + Altitude, data = df_vitd_60)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -58.880 -11.834  -1.393  10.236 129.025 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 88.6471036  1.8796153   47.16   <2e-16 ***
## Lat         -0.9820521  0.0804766  -12.20   <2e-16 ***
## Altitude    -0.0061546  0.0003536  -17.41   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.46 on 3227 degrees of freedom
## Multiple R-squared:  0.1076, Adjusted R-squared:  0.107 
## F-statistic: 194.5 on 2 and 3227 DF,  p-value: < 2.2e-16

Municipal-scale analysis

Pair-wise correlations

Deaths per 100,000

Altitude

Latitude

Ethnicity

Mean Vit D

nmol < 30

nmol < 50

nmol < 75

Multivariate regression 1

Response variable = mean Vit D
Explanatory variables = Deaths per 100,000, Altitude, Latitude, & Ethnicity

## 
## Call:
## lm(formula = mean_vitD ~ Deaths_ht + Alt + Lat + Ethnicity, data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.160  -3.660   0.121   3.444  17.820 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 88.6324511  4.0197833  22.049  < 2e-16 ***
## Deaths_ht   -0.0651842  0.0284848  -2.288   0.0236 *  
## Alt         -0.0064239  0.0005506 -11.667  < 2e-16 ***
## Lat         -0.8539272  0.1597550  -5.345 3.46e-07 ***
## Ethnicity   -0.0281777  0.0383905  -0.734   0.4642    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.551 on 144 degrees of freedom
## Multiple R-squared:  0.5684, Adjusted R-squared:  0.5564 
## F-statistic: 47.41 on 4 and 144 DF,  p-value: < 2.2e-16

Explanatory variables, together, explain 30% of the variance in Vit D at municipal scale. When controlling for other variables, each variable shows a negative relation with vit D, but only deaths per 100,000, altitude, and latitude are significant. If ethnicity is removed from the model, results are almost the same in terms of coefficients, their signs, and R2.

Multivariate regression 2

Response variable = Deaths per 100,000
Explanatory variables = Altitude and Latitude

## 
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat, data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.684 -10.062  -1.104   6.567  59.323 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -19.261431   8.301666  -2.320   0.0217 *  
## Alt           0.003873   0.001502   2.579   0.0109 *  
## Lat           2.038969   0.354502   5.752    5e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.13 on 146 degrees of freedom
## Multiple R-squared:  0.1922, Adjusted R-squared:  0.1811 
## F-statistic: 17.37 on 2 and 146 DF,  p-value: 1.712e-07

Multivariate regression 3

Response variable = Deaths per 100,000
Explanatory variables = Altitude, Latitude, nmol < 30

## 
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat + nmol_30, data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.302  -9.208  -1.610   6.945  56.432 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -15.085267   8.231551  -1.833  0.06891 .  
## Alt           0.002727   0.001519   1.795  0.07469 .  
## Lat           1.779544   0.357563   4.977 1.81e-06 ***
## nmol_30      88.665290  30.834252   2.876  0.00464 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.75 on 145 degrees of freedom
## Multiple R-squared:  0.2358, Adjusted R-squared:   0.22 
## F-statistic: 14.91 on 3 and 145 DF,  p-value: 1.637e-08